If a square a rectangle, then is a rectangle a square?
No. A square must be a rectangle, but a rectangle does not have to be a square. A square is a rectangle that has four sides of equal length. A rectangle MUST have the following: Four sidesFour angles that are right angles (90 degrees), so that the total is 360 degrees. Two pairs of parallel sides.Two pairs of equal sidesA square MUST have the following: Four sides (All must be the same length) Four angles(Must all be 90 degrees)Two pairs of parallel sides Because of that not all rectangles are squares but all squares are rectangles.Rectangles are parallelograms with all right angles, and opposite sides are congruent. Squares are parallelograms with all right angles, and ALL sides congruent. Therefore, all squares are rectangles, but not all rectangles are squares.False! squares have 4 equal sides and rectangles don't they only have 2 equal sides. Some rectangles are squares, but not all of them. On the other hand, all squares are rectangles.
Are all squares rectangles or are all rectangles squares?
You are mixed up ! All squares are rectangles, but not all rectangles are squares. A rectangle is a parallelogram with four congruent angles. A square is a parallelogram with four congruent angles and four congruent sides. A square is also a rhombus. Look at properies of quadrilaterals in your text book. QED
Are all squares kites but not rectangles?
Square: a regular quadrilateral, which means it has four equal sides and four equal angles.Rectangle: a quadrilateral with four equal angles.Kite: a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.It follows that the square is both a rectangle and a kite, while a rectangle might not be a kite and a kite might not be a rectangle. In fact, the only time a kite is also a rectangle is when the shape is a square.
Why is a rectangle not a square?
You state your question as if it is true that a rectangle is not a square. I don’t think you have given sufficient thought to the relationships between the quadrilaterals you have involved in your question.‘A rectangle is a quadrilateral with four right angles.’ This statement contains sufficient information for you to decide whether any quadrilateral is, or is not, a rectangle.‘A square is a rectangle which has all four of its sides of equal length.’ This statement, together with the previous one contains sufficient information for you to decide whether any quadrilateral is, or is not, a square.You will notice that neither statement says that of the four sides a rectangle has, one pair of parallel sides are of equal length and the other pair of parallel sides while also being of equal length are of a different length to the first pair. This is because they do not have to be different.So the 4 sides of a rectangle may, or may not be, of equal length. If they are of equal length, then THAT RECTANGLE IS A SQUARE. If the rectangle’s 2 pairs of parallel sides are not of equal length then THAT RECTANGLE IS NOT A SQUARE.So, to conclude: A RECTANGLE MAY OR MAY NOT BE A SQUARE, [ie, ALL SQUARES ARE RECTANGLES. SOME RECTANGLES ARE SQUARES.]Footnote 1: If you find the straightforward logic above difficult to come to terms with, then this is probably because you learned at an early age of the rectangle known colloquially as an OBLONG, in which one of the pairs of parallel sides are not the same length as the other pair, ie an oblong is a non-square rectangle.Footnote 2: Risking confusing the reader by adding the name of another quadrilateral, I will conclude by saying that all of the quadrilaterals named above are also parallelograms.
Is every square a rectangle?
Yes, if you use the definition of a rectangle to be a four-sided shape with each angle equal to ninety degrees. A square definitely fits that description, although a square has the additional constraint that each side is the same length.Squares can be considered a subset or subtype of rectangle. Some people do not consider squares rectangles, however. These people typically are not mathematicians.An interesting concept with squares is that they are also rhombuses (rhombi?). A rhombus is a four-sided shape where each side has the same length. A rectangle is not (necessarily) a rhombus. Therefore, squares have the property of multiple inheritance (which is more a computer science term than a math term).
True of False, All rectangles are squares?
False, all SQUARES are RECTANGLES, but not the other way around. A rectangle must have 4 right corners, with opposite sides having the same length, like a square. A square has to have all 4 sides equal.
Are all squares similar? Why? Are all rectangles similar? Why? Are all parallelograms similar? Why?
All squares are similar, the ratio of their side lengths is always 1:1:1:1 and all vertex angles are 90 degrees. Rectangles are not all similar because the ratios of the lengths of the pairs of sides can be anything, so some pairs of rectangles are not simple magnifications of each other. Parallelograms are not similar for the same reason. In addition, they can have different vertex angles, another source of 'dissimilarity'.